Search results for "convex variational problems"

showing 3 items of 3 documents

Solutions to the 1-harmonic flow with values into a hyper-octant of the N-sphere

2013

Abstract We announce existence results for the 1-harmonic flow from a domain of R m into the first hyper-octant of the N -dimensional unit sphere, under homogeneous Neumann boundary conditions. The arguments rely on a notion of “geodesic representative” of a BV-vector field on its jump set.

Unit spheren-sphereGeodesicApplied MathematicsMathematical analysisA domainharmonic flowsOctant (solid geometry)non-convex variational problems1-harmonic flowlower semi-continuity and relaxation; total variation flow; 1-harmonic flow; non-convex variational problems; image processing; geodesic; partial differential equations; harmonic flowsimage processingHomogeneoustotal variation flowNeumann boundary conditionJumppartial differential equationslower semi-continuity and relaxationgeodesicMathematics
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THE 1-HARMONIC FLOW WITH VALUES IN A HYPEROCTANT OF THE N-SPHERE

2014

We prove the existence of solutions to the 1-harmonic flow — that is, the formal gradient flow of the total variation of a vector field with respect to the [math] -distance — from a domain of [math] into a hyperoctant of the [math] -dimensional unit sphere, [math] , under homogeneous Neumann boundary conditions. In particular, we characterize the lower-order term appearing in the Euler–Lagrange formulation in terms of the “geodesic representative” of a BV-director field on its jump set. Such characterization relies on a lower semicontinuity argument which leads to a nontrivial and nonconvex minimization problem: to find a shortest path between two points on [math] with respect to a metric w…

Unit spherenonconvex variational problemsriemannian manifolds with boundaryGeodesicn-sphereharmonic flows68U1053C2253C4435K9235K67Neumann boundary conditionpartial differential equations49J45MathematicsNumerical Analysisnonlinear parabolic systems; lower semicontinuity and relaxation; total variation flow; 1-harmonic flow; image processing; harmonic flows; partial differential equations; image processing.; geodesics; riemannian manifolds with boundary; nonconvex variational problemslower semicontinuity and relaxation58E20Applied MathematicsMathematical analysis49Q201-harmonic flowimage processingFlow (mathematics)35K55Metric (mathematics)total variation flowVector fieldnonlinear parabolic systemsBalanced flowAnalysisgeodesics
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A posteriori error identities for nonlinear variational problems

2015

A posteriori error estimation methods are usually developed in the context of upper and lower bounds of errors. In this paper, we are concerned with a posteriori analysis in terms of identities, i.e., we deduce error relations, which holds as equalities. We discuss a general form of error identities for a wide class of convex variational problems. The left hand sides of these identities can be considered as certain measures of errors (expressed in terms of primal/dual solutions and respective approximations) while the right hand sides contain only known approximations. Finally, we consider several examples and show that in some simple cases these identities lead to generalized forms of the …

estimates of deviations from the exact solutionconvex variational problemslcsh:Mathematicsconvex variation problemsEstimates of deviations from the exact solutionerror measures for nonlinear problemserror measures for nonlinear problems.lcsh:QA1-939Mathematics and its Applications: Annals of the Academy of Romanian Scientists
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